This article considers a multilayered cloud-enabled HAPS network, similar to Fig. REF , consisting of \(B_A\)  hot-air balloons (HBSs) and \(B_T\)  terrestrial BSs (TBSs) connected to one cloud-enabled HAPS via high-speed FSO fronthaul links. All TBSs and HBSs are assumed to have limited transmit power and fronthaul capacity. Connecting all TBSs and HBSs to the HAPS cloud processor allows them to cooperate to serve all users. Although this approach reduces the interference drastically, it requires high fronthaul capacity, which can be physically infeasible [1]}. Therefore, we consider grouping the \(B = B_T + B_A\)  BSs, each equipped with \(M\)  antennas, into \(Q\)  mutually exclusive clusters; each cluster consists of \(L\)  BSs, where the BSs within each cluster can coordinate to serve their associated users in a network MIMO fashion to control the interference in the network. We classify the clusters as \(Q_A\)  hot-air balloons clusters and \(Q_T\)  terrestrial clusters. The grouping of BSs into mutually exclusive clusters is assumed to be fixed, and we denote the set of BSs in cluster \(q\)  by \(\mathcal {B}_q\) , where \( \cup _{q=1}^Q\mathcal {B}_q = \mathcal {B} \) . Let \(\mathcal {Q} = \mathcal {Q}_A \cup \mathcal {Q}_T\)  denote the set of all TBSs and HBSs clusters, where hot-air balloons and terrestrial sets are denoted by \(\mathcal {Q}_A\)  and \( \mathcal {Q}_T\) , respectively. Moreover, the paper assumes that there are \(U = U_T + U_A\)  single-antenna users, where \(U_T\)  is the number of terrestrial users and \(U_A\)  is the number of aerial/UAV users. The users are assumed to be separated via spatial multiplexing, i.e., through beamforming. Similarly, we denote the set of aerial and terrestrial users by \(\mathcal {U}_A\)  and \(\mathcal {U}_T\) , respectively, and their union by \(\mathcal {U}\) .
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